Question

The power generated by a windmill is a function of the speed wind. The approximate power is given by the function $P\left(s\right)=\frac{s^3}{1000}$, where $\left(s\right)$ represents the speed of the wind in kilometer per hour. Find the units of power $P\left(s\right)$ generated by the windmill when the wind speed is 18 kilometers per hour.

Short answer

The power $P\left(s\right)$ generated by the windmill is $5.832$.

Step-by-step solution

Step 1. Write down the given information.

The power $P\left(s\right)$ generated by the windmill as a function of speed wind $\left(s\right)$, is given as:

$P\left(s\right)=\frac{s^3}{1000}....\left(1\right)$

Step 2. Calculation.

The power $P\left(s\right)$ generated by the windmill as a function of speed wind when speed of wind $s=18km{h}^{-1}$, is evaluated by plugging $s=18$in (1).

$\begin{array}{c}P\left(18\right)=\frac{{\left(18\right)}^3}{1000}\\ =5.832\text{}\end{array}$

Step 3. Conclusion.

The power $P\left(s\right)$ generated by the windmill $5.832$.